A mop of this type is described in German registered utility model 76 25 260. The absorbent strips, which are fixed in the holding device essentially transversely to the longitudinal direction of the handle, are normally made of a formed cotton fabric. They have essentially no elasticity, particularly in the wet state, and hang down in a freely pendulous way similar to yarn strands. Because of the lack of fullness of the formed cotton fabric from which they are made, the resulting appearance seems meager. In addition, due to the swinging motion during the course of cleaning floors, there is a latent danger of contact between the plastic holding device and furniture or walls which can lead to mutual damage and is not very satisfactory.